I know mining is extremely difficult now. I just wondering has anyone "won" by solo mining a block? How does the chances compare against say wining the lottery? Assume 3 Giga Hashes Per Second say.
Unless the lucky winner were to announce his luck, there is no way for anyone to tell the difference. So, even if one cannot find any information suggesting that someone did, it could have happened.
Blockchain.info gives the current hashing power as 47,289,554.08 GHash/s, so your chance to mine any one block would be
3/47,289,554.0 = 6.3439e-8.
In Germany there is a popular lottery where you have to guess six out of 49 and one out of ten numbers. The chance of getting all seven numbers right is 7.1511e-8. So, the probability to win the jackpot is currently as likely as solo-mining a block with 3GHash/s. Of course, the lottery has a bunch of smaller prices for getting it partially right, and the jackpot would be worth millions of Euros, not 25 BTC.
But then, it is cheaper to play "Bitcoin lottery" and the draws are more frequent.
Below an estimate of the chance to get one block out of a day's/year's worth of blocks (disregarding increasing difficulty):
Altogether, it seems to me that regular lottery is more profitable, but then "Playing lottery is a tax for people that are bad at math.".
Here is a real world jackpot!